To help you in Q5 try to adress the following questions:
(-) How many classes does the DFA have?
(-) To check if u ~ v why is it sufficient to check whether u' ~ v' such that |u'|,|v'| <= m and the transition from u to u' and from v to v' are explicit (think about the definition of ~)?
(-) How many words of length at most m are there?

Try to adress (b) and (c) even if you did not explain (a) in detail…
The sole reason of part (a) is that you understand that in order to dsitinguish two SPECIFIC words, you need to do a finite (small) amount of work.